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A237260 Least positive integer m < n with prime(prime(m)) + 2 and prime(n-m) + 2 both prime, or 0 if such a number m does not exist. 3
0, 0, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 4, 23, 6, 1, 2, 1, 2, 3, 4, 7, 1, 2, 1, 2, 3, 4, 7, 6, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 4, 14, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 24, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Conjecture: a(n) < sqrt(6*n)*log(3*n) for all n > 0.

We have verified this for n up to 5*10^5. Note that a(273) = 271 > sqrt(6*273)*log(2*273).

According to the conjecture in A218829, a(n) should be positive for all n > 2.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

EXAMPLE

a(5) = 2 since prime(prime(2)) + 2 = prime(3) + 2 = 7 and prime(5-2) + 2 = 7 are both prime, but prime(5-1) + 2 = 7 + 2 = 9 is composite.

MATHEMATICA

pq[k_, m_]:=PrimeQ[Prime[k]+2]&&PrimeQ[Prime[Prime[m]]+2]

Do[Do[If[pq[n-m, m], Print[n, " ", m]; Goto[aa]], {m, 1, n-1}];

Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 70}]

CROSSREFS

Cf. A000040, A001359, A006512, A218829, A237259.

Sequence in context: A136314 A121997 A023128 * A249727 A023118 A122197

Adjacent sequences:  A237257 A237258 A237259 * A237261 A237262 A237263

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Feb 05 2014

STATUS

approved

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Last modified January 22 07:31 EST 2022. Contains 350481 sequences. (Running on oeis4.)